Symmetry 2014, 6(2), 396-408; doi:10.3390/sym6020396
Article

Invisibility and PT Symmetry: A Simple Geometrical Viewpoint

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Received: 24 February 2014; in revised form: 12 May 2014 / Accepted: 14 May 2014 / Published: 22 May 2014
(This article belongs to the Special Issue Physics based on Two-by-two Matrices)
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract: We give a simplified account of the properties of the transfer matrix for a complex one-dimensional potential, paying special attention to the particular instance of unidirectional invisibility. In appropriate variables, invisible potentials appear as performing null rotations, which lead to the helicity-gauge symmetry of massless particles. In hyperbolic geometry, this can be interpreted, via Möbius transformations, as parallel displacements, a geometric action that has no Euclidean analogy.
Keywords: ΡT symmetry; SL(2, C); Lorentz group; Hyperbolic geometry
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MDPI and ACS Style

Sánchez-Soto, L.L.; Monzón, J.J. Invisibility and PT Symmetry: A Simple Geometrical Viewpoint. Symmetry 2014, 6, 396-408.

AMA Style

Sánchez-Soto LL, Monzón JJ. Invisibility and PT Symmetry: A Simple Geometrical Viewpoint. Symmetry. 2014; 6(2):396-408.

Chicago/Turabian Style

Sánchez-Soto, Luis L.; Monzón, Juan J. 2014. "Invisibility and PT Symmetry: A Simple Geometrical Viewpoint." Symmetry 6, no. 2: 396-408.

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